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1999 OIM Problems/Problem 2

Revision as of 16:01, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Given two circles <math>M</math> and <math>N</math>, we say that <math>M</math> bisects <math>N</math> if the common chord is a diameter of <math>N</math>. Cons...")
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Problem

Given two circles $M$ and $N$, we say that $M$ bisects $N$ if the common chord is a diameter of $N$.

Consider two fixed non-concentric circles $C_1$ and $C_2$.

a) Prove that there are infinitely many circles $B$ such that $B$ bisects $C_1$ and $B$ bisects $C_2$.

b) Find the locus of the centers of circles $B$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe14.htm

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